nbtdedup.c

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/*-------------------------------------------------------------------------
 *
 * nbtdedup.c
 *    Deduplicate or bottom-up delete items in Postgres btrees.
 *
 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/access/nbtree/nbtdedup.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/nbtree.h"
#include "access/nbtxlog.h"
#include "miscadmin.h"
#include "utils/rel.h"

static void _bt_bottomupdel_finish_pending(Page page, BTDedupState state,
                                           TM_IndexDeleteOp *delstate);
static bool _bt_do_singleval(Relation rel, Page page, BTDedupState state,
                             OffsetNumber minoff, IndexTuple newitem);
static void _bt_singleval_fillfactor(Page page, BTDedupState state,
                                     Size newitemsz);
#ifdef USE_ASSERT_CHECKING
static bool _bt_posting_valid(IndexTuple posting);
#endif

/*
 * Perform a deduplication pass.
 *
 * The general approach taken here is to perform as much deduplication as
 * possible to free as much space as possible.  Note, however, that "single
 * value" strategy is used for !bottomupdedup callers when the page is full of
 * tuples of a single value.  Deduplication passes that apply the strategy
 * will leave behind a few untouched tuples at the end of the page, preparing
 * the page for an anticipated page split that uses nbtsplitloc.c's own single
 * value strategy.  Our high level goal is to delay merging the untouched
 * tuples until after the page splits.
 *
 * When a call to _bt_bottomupdel_pass() just took place (and failed), our
 * high level goal is to prevent a page split entirely by buying more time.
 * We still hope that a page split can be avoided altogether.  That's why
 * single value strategy is not even considered for bottomupdedup callers.
 *
 * The page will have to be split if we cannot successfully free at least
 * newitemsz (we also need space for newitem's line pointer, which isn't
 * included in caller's newitemsz).
 *
 * Note: Caller should have already deleted all existing items with their
 * LP_DEAD bits set.
 */
void
_bt_dedup_pass(Relation rel, Buffer buf, Relation heapRel, IndexTuple newitem,
               Size newitemsz, bool bottomupdedup)
{
    OffsetNumber offnum,
                minoff,
                maxoff;
    Page        page = BufferGetPage(buf);
    BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    Page        newpage;
    BTDedupState state;
    Size        pagesaving = 0;
    bool        singlevalstrat = false;
    int         nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);

    /* Passed-in newitemsz is MAXALIGNED but does not include line pointer */
    newitemsz += sizeof(ItemIdData);

    /*
     * Initialize deduplication state.
     *
     * It would be possible for maxpostingsize (limit on posting list tuple
     * size) to be set to one third of the page.  However, it seems like a
     * good idea to limit the size of posting lists to one sixth of a page.
     * That ought to leave us with a good split point when pages full of
     * duplicates can be split several times.
     */
    state = (BTDedupState) palloc(sizeof(BTDedupStateData));
    state->deduplicate = true;
    state->nmaxitems = 0;
    state->maxpostingsize = Min(BTMaxItemSize(page) / 2, INDEX_SIZE_MASK);
    /* Metadata about base tuple of current pending posting list */
    state->base = NULL;
    state->baseoff = InvalidOffsetNumber;
    state->basetupsize = 0;
    /* Metadata about current pending posting list TIDs */
    state->htids = palloc(state->maxpostingsize);
    state->nhtids = 0;
    state->nitems = 0;
    /* Size of all physical tuples to be replaced by pending posting list */
    state->phystupsize = 0;
    /* nintervals should be initialized to zero */
    state->nintervals = 0;

    minoff = P_FIRSTDATAKEY(opaque);
    maxoff = PageGetMaxOffsetNumber(page);

    /*
     * Consider applying "single value" strategy, though only if the page
     * seems likely to be split in the near future
     */
    if (!bottomupdedup)
        singlevalstrat = _bt_do_singleval(rel, page, state, minoff, newitem);

    /*
     * Deduplicate items from page, and write them to newpage.
     *
     * Copy the original page's LSN into newpage copy.  This will become the
     * updated version of the page.  We need this because XLogInsert will
     * examine the LSN and possibly dump it in a page image.
     */
    newpage = PageGetTempPageCopySpecial(page);
    PageSetLSN(newpage, PageGetLSN(page));

    /* Copy high key, if any */
    if (!P_RIGHTMOST(opaque))
    {
        ItemId      hitemid = PageGetItemId(page, P_HIKEY);
        Size        hitemsz = ItemIdGetLength(hitemid);
        IndexTuple  hitem = (IndexTuple) PageGetItem(page, hitemid);

        if (PageAddItem(newpage, (Item) hitem, hitemsz, P_HIKEY,
                        false, false) == InvalidOffsetNumber)
            elog(ERROR, "deduplication failed to add highkey");
    }

    for (offnum = minoff;
         offnum <= maxoff;
         offnum = OffsetNumberNext(offnum))
    {
        ItemId      itemid = PageGetItemId(page, offnum);
        IndexTuple  itup = (IndexTuple) PageGetItem(page, itemid);

        Assert(!ItemIdIsDead(itemid));

        if (offnum == minoff)
        {
            /*
             * No previous/base tuple for the data item -- use the data item
             * as base tuple of pending posting list
             */
            _bt_dedup_start_pending(state, itup, offnum);
        }
        else if (state->deduplicate &&
                 _bt_keep_natts_fast(rel, state->base, itup) > nkeyatts &&
                 _bt_dedup_save_htid(state, itup))
        {
            /*
             * Tuple is equal to base tuple of pending posting list.  Heap
             * TID(s) for itup have been saved in state.
             */
        }
        else
        {
            /*
             * Tuple is not equal to pending posting list tuple, or
             * _bt_dedup_save_htid() opted to not merge current item into
             * pending posting list for some other reason (e.g., adding more
             * TIDs would have caused posting list to exceed current
             * maxpostingsize).
             *
             * If state contains pending posting list with more than one item,
             * form new posting tuple, and actually update the page.  Else
             * reset the state and move on without modifying the page.
             */
            pagesaving += _bt_dedup_finish_pending(newpage, state);

            if (singlevalstrat)
            {
                /*
                 * Single value strategy's extra steps.
                 *
                 * Lower maxpostingsize for sixth and final large posting list
                 * tuple at the point where 5 maxpostingsize-capped tuples
                 * have either been formed or observed.
                 *
                 * When a sixth maxpostingsize-capped item is formed/observed,
                 * stop merging together tuples altogether.  The few tuples
                 * that remain at the end of the page won't be merged together
                 * at all (at least not until after a future page split takes
                 * place).
                 */
                if (state->nmaxitems == 5)
                    _bt_singleval_fillfactor(page, state, newitemsz);
                else if (state->nmaxitems == 6)
                {
                    state->deduplicate = false;
                    singlevalstrat = false; /* won't be back here */
                }
            }

            /* itup starts new pending posting list */
            _bt_dedup_start_pending(state, itup, offnum);
        }
    }

    /* Handle the last item */
    pagesaving += _bt_dedup_finish_pending(newpage, state);

    /*
     * If no items suitable for deduplication were found, newpage must be
     * exactly the same as the original page, so just return from function.
     *
     * We could determine whether or not to proceed on the basis the space
     * savings being sufficient to avoid an immediate page split instead.  We
     * don't do that because there is some small value in nbtsplitloc.c always
     * operating against a page that is fully deduplicated (apart from
     * newitem).  Besides, most of the cost has already been paid.
     */
    if (state->nintervals == 0)
    {
        /* cannot leak memory here */
        pfree(newpage);
        pfree(state->htids);
        pfree(state);
        return;
    }

    /*
     * By here, it's clear that deduplication will definitely go ahead.
     *
     * Clear the BTP_HAS_GARBAGE page flag.  The index must be a heapkeyspace
     * index, and as such we'll never pay attention to BTP_HAS_GARBAGE anyway.
     * But keep things tidy.
     */
    if (P_HAS_GARBAGE(opaque))
    {
        BTPageOpaque nopaque = (BTPageOpaque) PageGetSpecialPointer(newpage);

        nopaque->btpo_flags &= ~BTP_HAS_GARBAGE;
    }

    START_CRIT_SECTION();

    PageRestoreTempPage(newpage, page);
    MarkBufferDirty(buf);

    /* XLOG stuff */
    if (RelationNeedsWAL(rel))
    {
        XLogRecPtr  recptr;
        xl_btree_dedup xlrec_dedup;

        xlrec_dedup.nintervals = state->nintervals;

        XLogBeginInsert();
        XLogRegisterBuffer(0, buf, REGBUF_STANDARD);
        XLogRegisterData((char *) &xlrec_dedup, SizeOfBtreeDedup);

        /*
         * The intervals array is not in the buffer, but pretend that it is.
         * When XLogInsert stores the whole buffer, the array need not be
         * stored too.
         */
        XLogRegisterBufData(0, (char *) state->intervals,
                            state->nintervals * sizeof(BTDedupInterval));

        recptr = XLogInsert(RM_BTREE_ID, XLOG_BTREE_DEDUP);

        PageSetLSN(page, recptr);
    }

    END_CRIT_SECTION();

    /* Local space accounting should agree with page accounting */
    Assert(pagesaving < newitemsz || PageGetExactFreeSpace(page) >= newitemsz);

    /* cannot leak memory here */
    pfree(state->htids);
    pfree(state);
}

/*
 * Perform bottom-up index deletion pass.
 *
 * See if duplicate index tuples (plus certain nearby tuples) are eligible to
 * be deleted via bottom-up index deletion.  The high level goal here is to
 * entirely prevent "unnecessary" page splits caused by MVCC version churn
 * from UPDATEs (when the UPDATEs don't logically modify any of the columns
 * covered by the 'rel' index).  This is qualitative, not quantitative -- we
 * do not particularly care about once-off opportunities to delete many index
 * tuples together.
 *
 * See nbtree/README for details on the design of nbtree bottom-up deletion.
 * See access/tableam.h for a description of how we're expected to cooperate
 * with the tableam.
 *
 * Returns true on success, in which case caller can assume page split will be
 * avoided for a reasonable amount of time.  Returns false when caller should
 * deduplicate the page (if possible at all).
 *
 * Note: Occasionally we return true despite failing to delete enough items to
 * avoid a split.  This makes caller skip deduplication and go split the page
 * right away.  Our return value is always just advisory information.
 *
 * Note: Caller should have already deleted all existing items with their
 * LP_DEAD bits set.
 */
bool
_bt_bottomupdel_pass(Relation rel, Buffer buf, Relation heapRel,
                     Size newitemsz)
{
    OffsetNumber offnum,
                minoff,
                maxoff;
    Page        page = BufferGetPage(buf);
    BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);
    BTDedupState state;
    TM_IndexDeleteOp delstate;
    bool        neverdedup;
    int         nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);

    /* Passed-in newitemsz is MAXALIGNED but does not include line pointer */
    newitemsz += sizeof(ItemIdData);

    /* Initialize deduplication state */
    state = (BTDedupState) palloc(sizeof(BTDedupStateData));
    state->deduplicate = true;
    state->nmaxitems = 0;
    state->maxpostingsize = BLCKSZ; /* We're not really deduplicating */
    state->base = NULL;
    state->baseoff = InvalidOffsetNumber;
    state->basetupsize = 0;
    state->htids = palloc(state->maxpostingsize);
    state->nhtids = 0;
    state->nitems = 0;
    state->phystupsize = 0;
    state->nintervals = 0;

    /*
     * Initialize tableam state that describes bottom-up index deletion
     * operation.
     *
     * We'll go on to ask the tableam to search for TIDs whose index tuples we
     * can safely delete.  The tableam will search until our leaf page space
     * target is satisfied, or until the cost of continuing with the tableam
     * operation seems too high.  It focuses its efforts on TIDs associated
     * with duplicate index tuples that we mark "promising".
     *
     * This space target is a little arbitrary.  The tableam must be able to
     * keep the costs and benefits in balance.  We provide the tableam with
     * exhaustive information about what might work, without directly
     * concerning ourselves with avoiding work during the tableam call.  Our
     * role in costing the bottom-up deletion process is strictly advisory.
     */
    delstate.bottomup = true;
    delstate.bottomupfreespace = Max(BLCKSZ / 16, newitemsz);
    delstate.ndeltids = 0;
    delstate.deltids = palloc(MaxTIDsPerBTreePage * sizeof(TM_IndexDelete));
    delstate.status = palloc(MaxTIDsPerBTreePage * sizeof(TM_IndexStatus));

    minoff = P_FIRSTDATAKEY(opaque);
    maxoff = PageGetMaxOffsetNumber(page);
    for (offnum = minoff;
         offnum <= maxoff;
         offnum = OffsetNumberNext(offnum))
    {
        ItemId      itemid = PageGetItemId(page, offnum);
        IndexTuple  itup = (IndexTuple) PageGetItem(page, itemid);

        Assert(!ItemIdIsDead(itemid));

        if (offnum == minoff)
        {
            /* itup starts first pending interval */
            _bt_dedup_start_pending(state, itup, offnum);
        }
        else if (_bt_keep_natts_fast(rel, state->base, itup) > nkeyatts &&
                 _bt_dedup_save_htid(state, itup))
        {
            /* Tuple is equal; just added its TIDs to pending interval */
        }
        else
        {
            /* Finalize interval -- move its TIDs to delete state */
            _bt_bottomupdel_finish_pending(page, state, &delstate);

            /* itup starts new pending interval */
            _bt_dedup_start_pending(state, itup, offnum);
        }
    }
    /* Finalize final interval -- move its TIDs to delete state */
    _bt_bottomupdel_finish_pending(page, state, &delstate);

    /*
     * We don't give up now in the event of having few (or even zero)
     * promising tuples for the tableam because it's not up to us as the index
     * AM to manage costs (note that the tableam might have heuristics of its
     * own that work out what to do).  We should at least avoid having our
     * caller do a useless deduplication pass after we return in the event of
     * zero promising tuples, though.
     */
    neverdedup = false;
    if (state->nintervals == 0)
        neverdedup = true;

    pfree(state->htids);
    pfree(state);

    /* Ask tableam which TIDs are deletable, then physically delete them */
    _bt_delitems_delete_check(rel, buf, heapRel, &delstate);

    pfree(delstate.deltids);
    pfree(delstate.status);

    /* Report "success" to caller unconditionally to avoid deduplication */
    if (neverdedup)
        return true;

    /* Don't dedup when we won't end up back here any time soon anyway */
    return PageGetExactFreeSpace(page) >= Max(BLCKSZ / 24, newitemsz);
}

/*
 * Create a new pending posting list tuple based on caller's base tuple.
 *
 * Every tuple processed by deduplication either becomes the base tuple for a
 * posting list, or gets its heap TID(s) accepted into a pending posting list.
 * A tuple that starts out as the base tuple for a posting list will only
 * actually be rewritten within _bt_dedup_finish_pending() when it turns out
 * that there are duplicates that can be merged into the base tuple.
 */
void
_bt_dedup_start_pending(BTDedupState state, IndexTuple base,
                        OffsetNumber baseoff)
{
    Assert(state->nhtids == 0);
    Assert(state->nitems == 0);
    Assert(!BTreeTupleIsPivot(base));

    /*
     * Copy heap TID(s) from new base tuple for new candidate posting list
     * into working state's array
     */
    if (!BTreeTupleIsPosting(base))
    {
        memcpy(state->htids, &base->t_tid, sizeof(ItemPointerData));
        state->nhtids = 1;
        state->basetupsize = IndexTupleSize(base);
    }
    else
    {
        int         nposting;

        nposting = BTreeTupleGetNPosting(base);
        memcpy(state->htids, BTreeTupleGetPosting(base),
               sizeof(ItemPointerData) * nposting);
        state->nhtids = nposting;
        /* basetupsize should not include existing posting list */
        state->basetupsize = BTreeTupleGetPostingOffset(base);
    }

    /*
     * Save new base tuple itself -- it'll be needed if we actually create a
     * new posting list from new pending posting list.
     *
     * Must maintain physical size of all existing tuples (including line
     * pointer overhead) so that we can calculate space savings on page.
     */
    state->nitems = 1;
    state->base = base;
    state->baseoff = baseoff;
    state->phystupsize = MAXALIGN(IndexTupleSize(base)) + sizeof(ItemIdData);
    /* Also save baseoff in pending state for interval */
    state->intervals[state->nintervals].baseoff = state->baseoff;
}

/*
 * Save itup heap TID(s) into pending posting list where possible.
 *
 * Returns bool indicating if the pending posting list managed by state now
 * includes itup's heap TID(s).
 */
bool
_bt_dedup_save_htid(BTDedupState state, IndexTuple itup)
{
    int         nhtids;
    ItemPointer htids;
    Size        mergedtupsz;

    Assert(!BTreeTupleIsPivot(itup));

    if (!BTreeTupleIsPosting(itup))
    {
        nhtids = 1;
        htids = &itup->t_tid;
    }
    else
    {
        nhtids = BTreeTupleGetNPosting(itup);
        htids = BTreeTupleGetPosting(itup);
    }

    /*
     * Don't append (have caller finish pending posting list as-is) if
     * appending heap TID(s) from itup would put us over maxpostingsize limit.
     *
     * This calculation needs to match the code used within _bt_form_posting()
     * for new posting list tuples.
     */
    mergedtupsz = MAXALIGN(state->basetupsize +
                           (state->nhtids + nhtids) * sizeof(ItemPointerData));

    if (mergedtupsz > state->maxpostingsize)
    {
        /*
         * Count this as an oversized item for single value strategy, though
         * only when there are 50 TIDs in the final posting list tuple.  This
         * limit (which is fairly arbitrary) avoids confusion about how many
         * 1/6 of a page tuples have been encountered/created by the current
         * deduplication pass.
         *
         * Note: We deliberately don't consider which deduplication pass
         * merged together tuples to create this item (could be a previous
         * deduplication pass, or current pass).  See _bt_do_singleval()
         * comments.
         */
        if (state->nhtids > 50)
            state->nmaxitems++;

        return false;
    }

    /*
     * Save heap TIDs to pending posting list tuple -- itup can be merged into
     * pending posting list
     */
    state->nitems++;
    memcpy(state->htids + state->nhtids, htids,
           sizeof(ItemPointerData) * nhtids);
    state->nhtids += nhtids;
    state->phystupsize += MAXALIGN(IndexTupleSize(itup)) + sizeof(ItemIdData);

    return true;
}

/*
 * Finalize pending posting list tuple, and add it to the page.  Final tuple
 * is based on saved base tuple, and saved list of heap TIDs.
 *
 * Returns space saving from deduplicating to make a new posting list tuple.
 * Note that this includes line pointer overhead.  This is zero in the case
 * where no deduplication was possible.
 */
Size
_bt_dedup_finish_pending(Page newpage, BTDedupState state)
{
    OffsetNumber tupoff;
    Size        tuplesz;
    Size        spacesaving;

    Assert(state->nitems > 0);
    Assert(state->nitems <= state->nhtids);
    Assert(state->intervals[state->nintervals].baseoff == state->baseoff);

    tupoff = OffsetNumberNext(PageGetMaxOffsetNumber(newpage));
    if (state->nitems == 1)
    {
        /* Use original, unchanged base tuple */
        tuplesz = IndexTupleSize(state->base);
        if (PageAddItem(newpage, (Item) state->base, tuplesz, tupoff,
                        false, false) == InvalidOffsetNumber)
            elog(ERROR, "deduplication failed to add tuple to page");

        spacesaving = 0;
    }
    else
    {
        IndexTuple  final;

        /* Form a tuple with a posting list */
        final = _bt_form_posting(state->base, state->htids, state->nhtids);
        tuplesz = IndexTupleSize(final);
        Assert(tuplesz <= state->maxpostingsize);

        /* Save final number of items for posting list */
        state->intervals[state->nintervals].nitems = state->nitems;

        Assert(tuplesz == MAXALIGN(IndexTupleSize(final)));
        if (PageAddItem(newpage, (Item) final, tuplesz, tupoff, false,
                        false) == InvalidOffsetNumber)
            elog(ERROR, "deduplication failed to add tuple to page");

        pfree(final);
        spacesaving = state->phystupsize - (tuplesz + sizeof(ItemIdData));
        /* Increment nintervals, since we wrote a new posting list tuple */
        state->nintervals++;
        Assert(spacesaving > 0 && spacesaving < BLCKSZ);
    }

    /* Reset state for next pending posting list */
    state->nhtids = 0;
    state->nitems = 0;
    state->phystupsize = 0;

    return spacesaving;
}

/*
 * Finalize interval during bottom-up index deletion.
 *
 * During a bottom-up pass we expect that TIDs will be recorded in dedup state
 * first, and then get moved over to delstate (in variable-sized batches) by
 * calling here.  Call here happens when the number of TIDs in a dedup
 * interval is known, and interval gets finalized (i.e. when caller sees next
 * tuple on the page is not a duplicate, or when caller runs out of tuples to
 * process from leaf page).
 *
 * This is where bottom-up deletion determines and remembers which entries are
 * duplicates.  This will be important information to the tableam delete
 * infrastructure later on.  Plain index tuple duplicates are marked
 * "promising" here, per tableam contract.
 *
 * Our approach to marking entries whose TIDs come from posting lists is more
 * complicated.  Posting lists can only be formed by a deduplication pass (or
 * during an index build), so recent version churn affecting the pointed-to
 * logical rows is not particularly likely.  We may still give a weak signal
 * about posting list tuples' entries (by marking just one of its TIDs/entries
 * promising), though this is only a possibility in the event of further
 * duplicate index tuples in final interval that covers posting list tuple (as
 * in the plain tuple case).  A weak signal/hint will be useful to the tableam
 * when it has no stronger signal to go with for the deletion operation as a
 * whole.
 *
 * The heuristics we use work well in practice because we only need to give
 * the tableam the right _general_ idea about where to look.  Garbage tends to
 * naturally get concentrated in relatively few table blocks with workloads
 * that bottom-up deletion targets.  The tableam cannot possibly rank all
 * available table blocks sensibly based on the hints we provide, but that's
 * okay -- only the extremes matter.  The tableam just needs to be able to
 * predict which few table blocks will have the most tuples that are safe to
 * delete for each deletion operation, with low variance across related
 * deletion operations.
 */
static void
_bt_bottomupdel_finish_pending(Page page, BTDedupState state,
                               TM_IndexDeleteOp *delstate)
{
    bool        dupinterval = (state->nitems > 1);

    Assert(state->nitems > 0);
    Assert(state->nitems <= state->nhtids);
    Assert(state->intervals[state->nintervals].baseoff == state->baseoff);

    for (int i = 0; i < state->nitems; i++)
    {
        OffsetNumber offnum = state->baseoff + i;
        ItemId      itemid = PageGetItemId(page, offnum);
        IndexTuple  itup = (IndexTuple) PageGetItem(page, itemid);
        TM_IndexDelete *ideltid = &delstate->deltids[delstate->ndeltids];
        TM_IndexStatus *istatus = &delstate->status[delstate->ndeltids];

        if (!BTreeTupleIsPosting(itup))
        {
            /* Simple case: A plain non-pivot tuple */
            ideltid->tid = itup->t_tid;
            ideltid->id = delstate->ndeltids;
            istatus->idxoffnum = offnum;
            istatus->knowndeletable = false;    /* for now */
            istatus->promising = dupinterval;   /* simple rule */
            istatus->freespace = ItemIdGetLength(itemid) + sizeof(ItemIdData);

            delstate->ndeltids++;
        }
        else
        {
            /*
             * Complicated case: A posting list tuple.
             *
             * We make the conservative assumption that there can only be at
             * most one affected logical row per posting list tuple.  There
             * will be at most one promising entry in deltids to represent
             * this presumed lone logical row.  Note that this isn't even
             * considered unless the posting list tuple is also in an interval
             * of duplicates -- this complicated rule is just a variant of the
             * simple rule used to decide if plain index tuples are promising.
             */
            int         nitem = BTreeTupleGetNPosting(itup);
            bool        firstpromising = false;
            bool        lastpromising = false;

            Assert(_bt_posting_valid(itup));

            if (dupinterval)
            {
                /*
                 * Complicated rule: either the first or last TID in the
                 * posting list gets marked promising (if any at all)
                 */
                BlockNumber minblocklist,
                            midblocklist,
                            maxblocklist;
                ItemPointer mintid,
                            midtid,
                            maxtid;

                mintid = BTreeTupleGetHeapTID(itup);
                midtid = BTreeTupleGetPostingN(itup, nitem / 2);
                maxtid = BTreeTupleGetMaxHeapTID(itup);
                minblocklist = ItemPointerGetBlockNumber(mintid);
                midblocklist = ItemPointerGetBlockNumber(midtid);
                maxblocklist = ItemPointerGetBlockNumber(maxtid);

                /* Only entry with predominant table block can be promising */
                firstpromising = (minblocklist == midblocklist);
                lastpromising = (!firstpromising &&
                                 midblocklist == maxblocklist);
            }

            for (int p = 0; p < nitem; p++)
            {
                ItemPointer htid = BTreeTupleGetPostingN(itup, p);

                ideltid->tid = *htid;
                ideltid->id = delstate->ndeltids;
                istatus->idxoffnum = offnum;
                istatus->knowndeletable = false;    /* for now */
                istatus->promising = false;
                if ((firstpromising && p == 0) ||
                    (lastpromising && p == nitem - 1))
                    istatus->promising = true;
                istatus->freespace = sizeof(ItemPointerData);   /* at worst */

                ideltid++;
                istatus++;
                delstate->ndeltids++;
            }
        }
    }

    if (dupinterval)
    {
        state->intervals[state->nintervals].nitems = state->nitems;
        state->nintervals++;
    }

    /* Reset state for next interval */
    state->nhtids = 0;
    state->nitems = 0;
    state->phystupsize = 0;
}

/*
 * Determine if page non-pivot tuples (data items) are all duplicates of the
 * same value -- if they are, deduplication's "single value" strategy should
 * be applied.  The general goal of this strategy is to ensure that
 * nbtsplitloc.c (which uses its own single value strategy) will find a useful
 * split point as further duplicates are inserted, and successive rightmost
 * page splits occur among pages that store the same duplicate value.  When
 * the page finally splits, it should end up BTREE_SINGLEVAL_FILLFACTOR% full,
 * just like it would if deduplication were disabled.
 *
 * We expect that affected workloads will require _several_ single value
 * strategy deduplication passes (over a page that only stores duplicates)
 * before the page is finally split.  The first deduplication pass should only
 * find regular non-pivot tuples.  Later deduplication passes will find
 * existing maxpostingsize-capped posting list tuples, which must be skipped
 * over.  The penultimate pass is generally the first pass that actually
 * reaches _bt_singleval_fillfactor(), and so will deliberately leave behind a
 * few untouched non-pivot tuples.  The final deduplication pass won't free
 * any space -- it will skip over everything without merging anything (it
 * retraces the steps of the penultimate pass).
 *
 * Fortunately, having several passes isn't too expensive.  Each pass (after
 * the first pass) won't spend many cycles on the large posting list tuples
 * left by previous passes.  Each pass will find a large contiguous group of
 * smaller duplicate tuples to merge together at the end of the page.
 */
static bool
_bt_do_singleval(Relation rel, Page page, BTDedupState state,
                 OffsetNumber minoff, IndexTuple newitem)
{
    int         nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
    ItemId      itemid;
    IndexTuple  itup;

    itemid = PageGetItemId(page, minoff);
    itup = (IndexTuple) PageGetItem(page, itemid);

    if (_bt_keep_natts_fast(rel, newitem, itup) > nkeyatts)
    {
        itemid = PageGetItemId(page, PageGetMaxOffsetNumber(page));
        itup = (IndexTuple) PageGetItem(page, itemid);

        if (_bt_keep_natts_fast(rel, newitem, itup) > nkeyatts)
            return true;
    }

    return false;
}

/*
 * Lower maxpostingsize when using "single value" strategy, to avoid a sixth
 * and final maxpostingsize-capped tuple.  The sixth and final posting list
 * tuple will end up somewhat smaller than the first five.  (Note: The first
 * five tuples could actually just be very large duplicate tuples that
 * couldn't be merged together at all.  Deduplication will simply not modify
 * the page when that happens.)
 *
 * When there are six posting lists on the page (after current deduplication
 * pass goes on to create/observe a sixth very large tuple), caller should end
 * its deduplication pass.  It isn't useful to try to deduplicate items that
 * are supposed to end up on the new right sibling page following the
 * anticipated page split.  A future deduplication pass of future right
 * sibling page might take care of it.  (This is why the first single value
 * strategy deduplication pass for a given leaf page will generally find only
 * plain non-pivot tuples -- see _bt_do_singleval() comments.)
 */
static void
_bt_singleval_fillfactor(Page page, BTDedupState state, Size newitemsz)
{
    Size        leftfree;
    int         reduction;

    /* This calculation needs to match nbtsplitloc.c */
    leftfree = PageGetPageSize(page) - SizeOfPageHeaderData -
        MAXALIGN(sizeof(BTPageOpaqueData));
    /* Subtract size of new high key (includes pivot heap TID space) */
    leftfree -= newitemsz + MAXALIGN(sizeof(ItemPointerData));

    /*
     * Reduce maxpostingsize by an amount equal to target free space on left
     * half of page
     */
    reduction = leftfree * ((100 - BTREE_SINGLEVAL_FILLFACTOR) / 100.0);
    if (state->maxpostingsize > reduction)
        state->maxpostingsize -= reduction;
    else
        state->maxpostingsize = 0;
}

/*
 * Build a posting list tuple based on caller's "base" index tuple and list of
 * heap TIDs.  When nhtids == 1, builds a standard non-pivot tuple without a
 * posting list. (Posting list tuples can never have a single heap TID, partly
 * because that ensures that deduplication always reduces final MAXALIGN()'d
 * size of entire tuple.)
 *
 * Convention is that posting list starts at a MAXALIGN()'d offset (rather
 * than a SHORTALIGN()'d offset), in line with the approach taken when
 * appending a heap TID to new pivot tuple/high key during suffix truncation.
 * This sometimes wastes a little space that was only needed as alignment
 * padding in the original tuple.  Following this convention simplifies the
 * space accounting used when deduplicating a page (the same convention
 * simplifies the accounting for choosing a point to split a page at).
 *
 * Note: Caller's "htids" array must be unique and already in ascending TID
 * order.  Any existing heap TIDs from "base" won't automatically appear in
 * returned posting list tuple (they must be included in htids array.)
 */
IndexTuple
_bt_form_posting(IndexTuple base, ItemPointer htids, int nhtids)
{
    uint32      keysize,
                newsize;
    IndexTuple  itup;

    if (BTreeTupleIsPosting(base))
        keysize = BTreeTupleGetPostingOffset(base);
    else
        keysize = IndexTupleSize(base);

    Assert(!BTreeTupleIsPivot(base));
    Assert(nhtids > 0 && nhtids <= PG_UINT16_MAX);
    Assert(keysize == MAXALIGN(keysize));

    /* Determine final size of new tuple */
    if (nhtids > 1)
        newsize = MAXALIGN(keysize +
                           nhtids * sizeof(ItemPointerData));
    else
        newsize = keysize;

    Assert(newsize <= INDEX_SIZE_MASK);
    Assert(newsize == MAXALIGN(newsize));

    /* Allocate memory using palloc0() (matches index_form_tuple()) */
    itup = palloc0(newsize);
    memcpy(itup, base, keysize);
    itup->t_info &= ~INDEX_SIZE_MASK;
    itup->t_info |= newsize;
    if (nhtids > 1)
    {
        /* Form posting list tuple */
        BTreeTupleSetPosting(itup, nhtids, keysize);
        memcpy(BTreeTupleGetPosting(itup), htids,
               sizeof(ItemPointerData) * nhtids);
        Assert(_bt_posting_valid(itup));
    }
    else
    {
        /* Form standard non-pivot tuple */
        itup->t_info &= ~INDEX_ALT_TID_MASK;
        ItemPointerCopy(htids, &itup->t_tid);
        Assert(ItemPointerIsValid(&itup->t_tid));
    }

    return itup;
}

/*
 * Generate a replacement tuple by "updating" a posting list tuple so that it
 * no longer has TIDs that need to be deleted.
 *
 * Used by both VACUUM and index deletion.  Caller's vacposting argument
 * points to the existing posting list tuple to be updated.
 *
 * On return, caller's vacposting argument will point to final "updated"
 * tuple, which will be palloc()'d in caller's memory context.
 */
void
_bt_update_posting(BTVacuumPosting vacposting)
{
    IndexTuple  origtuple = vacposting->itup;
    uint32      keysize,
                newsize;
    IndexTuple  itup;
    int         nhtids;
    int         ui,
                d;
    ItemPointer htids;

    nhtids = BTreeTupleGetNPosting(origtuple) - vacposting->ndeletedtids;

    Assert(_bt_posting_valid(origtuple));
    Assert(nhtids > 0 && nhtids < BTreeTupleGetNPosting(origtuple));

    /*
     * Determine final size of new tuple.
     *
     * This calculation needs to match the code used within _bt_form_posting()
     * for new posting list tuples.  We avoid calling _bt_form_posting() here
     * to save ourselves a second memory allocation for a htids workspace.
     */
    keysize = BTreeTupleGetPostingOffset(origtuple);
    if (nhtids > 1)
        newsize = MAXALIGN(keysize +
                           nhtids * sizeof(ItemPointerData));
    else
        newsize = keysize;

    Assert(newsize <= INDEX_SIZE_MASK);
    Assert(newsize == MAXALIGN(newsize));

    /* Allocate memory using palloc0() (matches index_form_tuple()) */
    itup = palloc0(newsize);
    memcpy(itup, origtuple, keysize);
    itup->t_info &= ~INDEX_SIZE_MASK;
    itup->t_info |= newsize;

    if (nhtids > 1)
    {
        /* Form posting list tuple */
        BTreeTupleSetPosting(itup, nhtids, keysize);
        htids = BTreeTupleGetPosting(itup);
    }
    else
    {
        /* Form standard non-pivot tuple */
        itup->t_info &= ~INDEX_ALT_TID_MASK;
        htids = &itup->t_tid;
    }

    ui = 0;
    d = 0;
    for (int i = 0; i < BTreeTupleGetNPosting(origtuple); i++)
    {
        if (d < vacposting->ndeletedtids && vacposting->deletetids[d] == i)
        {
            d++;
            continue;
        }
        htids[ui++] = *BTreeTupleGetPostingN(origtuple, i);
    }
    Assert(ui == nhtids);
    Assert(d == vacposting->ndeletedtids);
    Assert(nhtids == 1 || _bt_posting_valid(itup));
    Assert(nhtids > 1 || ItemPointerIsValid(&itup->t_tid));

    /* vacposting arg's itup will now point to updated version */
    vacposting->itup = itup;
}

/*
 * Prepare for a posting list split by swapping heap TID in newitem with heap
 * TID from original posting list (the 'oposting' heap TID located at offset
 * 'postingoff').  Modifies newitem, so caller should pass their own private
 * copy that can safely be modified.
 *
 * Returns new posting list tuple, which is palloc()'d in caller's context.
 * This is guaranteed to be the same size as 'oposting'.  Modified newitem is
 * what caller actually inserts. (This happens inside the same critical
 * section that performs an in-place update of old posting list using new
 * posting list returned here.)
 *
 * While the keys from newitem and oposting must be opclass equal, and must
 * generate identical output when run through the underlying type's output
 * function, it doesn't follow that their representations match exactly.
 * Caller must avoid assuming that there can't be representational differences
 * that make datums from oposting bigger or smaller than the corresponding
 * datums from newitem.  For example, differences in TOAST input state might
 * break a faulty assumption about tuple size (the executor is entitled to
 * apply TOAST compression based on its own criteria).  It also seems possible
 * that further representational variation will be introduced in the future,
 * in order to support nbtree features like page-level prefix compression.
 *
 * See nbtree/README for details on the design of posting list splits.
 */
IndexTuple
_bt_swap_posting(IndexTuple newitem, IndexTuple oposting, int postingoff)
{
    int         nhtids;
    char       *replacepos;
    char       *replaceposright;
    Size        nmovebytes;
    IndexTuple  nposting;

    nhtids = BTreeTupleGetNPosting(oposting);
    Assert(_bt_posting_valid(oposting));

    /*
     * The postingoff argument originated as a _bt_binsrch_posting() return
     * value.  It will be 0 in the event of corruption that makes a leaf page
     * contain a non-pivot tuple that's somehow identical to newitem (no two
     * non-pivot tuples should ever have the same TID).  This has been known
     * to happen in the field from time to time.
     *
     * Perform a basic sanity check to catch this case now.
     */
    if (!(postingoff > 0 && postingoff < nhtids))
        elog(ERROR, "posting list tuple with %d items cannot be split at offset %d",
             nhtids, postingoff);

    /*
     * Move item pointers in posting list to make a gap for the new item's
     * heap TID.  We shift TIDs one place to the right, losing original
     * rightmost TID. (nmovebytes must not include TIDs to the left of
     * postingoff, nor the existing rightmost/max TID that gets overwritten.)
     */
    nposting = CopyIndexTuple(oposting);
    replacepos = (char *) BTreeTupleGetPostingN(nposting, postingoff);
    replaceposright = (char *) BTreeTupleGetPostingN(nposting, postingoff + 1);
    nmovebytes = (nhtids - postingoff - 1) * sizeof(ItemPointerData);
    memmove(replaceposright, replacepos, nmovebytes);

    /* Fill the gap at postingoff with TID of new item (original new TID) */
    Assert(!BTreeTupleIsPivot(newitem) && !BTreeTupleIsPosting(newitem));
    ItemPointerCopy(&newitem->t_tid, (ItemPointer) replacepos);

    /* Now copy oposting's rightmost/max TID into new item (final new TID) */
    ItemPointerCopy(BTreeTupleGetMaxHeapTID(oposting), &newitem->t_tid);

    Assert(ItemPointerCompare(BTreeTupleGetMaxHeapTID(nposting),
                              BTreeTupleGetHeapTID(newitem)) < 0);
    Assert(_bt_posting_valid(nposting));

    return nposting;
}

/*
 * Verify posting list invariants for "posting", which must be a posting list
 * tuple.  Used within assertions.
 */
#ifdef USE_ASSERT_CHECKING
static bool
_bt_posting_valid(IndexTuple posting)
{
    ItemPointerData last;
    ItemPointer htid;

    if (!BTreeTupleIsPosting(posting) || BTreeTupleGetNPosting(posting) < 2)
        return false;

    /* Remember first heap TID for loop */
    ItemPointerCopy(BTreeTupleGetHeapTID(posting), &last);
    if (!ItemPointerIsValid(&last))
        return false;

    /* Iterate, starting from second TID */
    for (int i = 1; i < BTreeTupleGetNPosting(posting); i++)
    {
        htid = BTreeTupleGetPostingN(posting, i);

        if (!ItemPointerIsValid(htid))
            return false;
        if (ItemPointerCompare(htid, &last) <= 0)
            return false;
        ItemPointerCopy(htid, &last);
    }

    return true;
}
#endif